Mssbauer spectroscopy and transition metal chemistry fundamentals and applications

Moăssbauer Spectroscopy and Transition Metal Chemistry Philipp Guătlich Eckhard Bill Alfred X Trautwein l l Moăssbauer Spectroscopy and Transition Metal Chemistry Fundamentals and Applications with electronic supplementary material at extras.springer.com Prof Dr Philipp Guătlich Universitaăt Mainz Inst Anorganische und Analytische Chemie Staudingerweg 55099 Mainz Germany guetlich@uni-mainz.de Dr Eckhard Bill MPI fuăr Bioanorganische Chemie Stiftstr 34-36 45470 Muălheim Germany bill@mpi-muelheim.mpg.de Prof Dr Alfred X Trautwein Universitaăt zu Luăbeck Inst Physik Ratzeburger Allee 160 23538 Luăbeck Germany trautwein@physik.uni-luebeck.de Additional material to this book is available on CD-ROM; in subsequent printings this material can be downloaded from http://extras.springer.com using the following password: 978-3-540-88427-9 ISBN 978-3-540-88427-9 e-ISBN 978-3-540-88428-6 DOI 10.1007/978-3-540-88428-6 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010927411 # Springer‐Verlag Berlin Heidelberg 2011 This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Cover image: The picture shows a roman mask after restoration at the Roman-German Museum of Mainz The mask originates from the roman aera and had fallen into many fragments which were found mixed together with fragments from other iron-containing items such as weapons With the help of Moăssbauer spectroscopy (57Fe) the fragments belonging to the mask could be identified for successful restoration (P Guătlich, G Klingelhofer, P de Souza, unpublished) Cover design: Kuenkel Lopka GmbH, Heidelberg, Germany Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface More than five decades have passed since the young German physicist Rudolf L M€ ossbauer discovered the recoilless nuclear resonance (absorption) fluorescence of g-radiation The spectroscopic method based on this resonance effect – referred to as M€ossbauer spectroscopy – has subsequently developed into a powerful tool in solid-state research The users are chemists, physicists, biologists, geologists, and scientists from other disciplines, and the spectrum of problems amenable to this method has become extraordinarily broad Up to now, more than 60,000 reports have appeared in the literature dealing with applications of the M€ossbauer effect in the characterization of a vast variety of materials Besides many workshops, seminars, and symposia, a biannual conference series called The International Conference on the Applications of the M€ossbauer Effect (ICAME) started in 1960 (Urbana, USA) and regularly brings together scientists who are actively working on fundamental – as well as industrial – applications of the M€ ossbauer effect Undoubtedly, M€ ossbauer spectroscopy has taken its place as an important analytical tool among other physical methods of solid-state research By the same token, high-level education in solid-state physics, chemistry, and materials science in the broadest sense is strongly encouraged to dedicate sufficient space in the curriculum to this versatile method The main objective of this book is to assist the fulfillment of this purpose Many monographs and review articles on the principles and applications of M€ossbauer spectroscopy have appeared in the literature in the past However, significant developments regarding instrumentation, methodology, and theory related to M€ ossbauer spectroscopy, have been communicated recently, which have widened the applicability and thus, merit in our opinion, the necessity of updating the introductory literature We have tried to present a state-of-the-art book which concentrates on teaching the fundamentals, using theory as much as needed and as little as possible, and on practical applications Some parts of the book are based on the first edition published in 1978 in the Springer series “Inorganic Chemistry Concepts by P Guătlich, R Link, and A.X Trautwein Major updates have been included on practical aspects of measurements, on the computation of M€ossbauer v vi Preface parameters with modern quantum chemical techniques (special chapter by guestauthors F Neese and T Petrenko), on treating magnetic relaxation phenomena (special chapter by guest-author S Morup), selected applications in coordination chemistry, the use of synchrotron radiation to observe nuclear forward scattering (NFS) and inelastic scattering (NIS), and on the miniaturization of a M€ossbauer spectrometer for mobile spectroscopy in space and on earth (by guest-authors G Klingelh€ ofer and Iris Fleischer) The first five chapters are directed to the reader who is not familiar with the technique and deal with the basic principles of the recoilless nuclear resonance and essential aspects concerning measurements and the hyperfine interactions between nuclear moments and electric and magnetic fields Chapter by guest-authors F Neese and T Petrenko focuses on the computation and interpretation of M€ossbauer parameters such as isomer shift, electric quadrupole splitting, and magnetic dipole splitting using modern DFT methods Chapter 6, written by guest-author S Morup, describes how magnetic relaxation phenomena can influence the shape of (mainly 57 Fe) M€ ossbauer spectra Chapter presents an up-to-date summary of the work on all M€ ossbauer-active transition metal elements in accordance with the title of this book This chapter will be particularly useful for those who are actively concerned with M€ ossbauer work on noniron transition elements We are certainly aware of the large amount of excellent M€ ossbauer spectroscopy involving other M€ossbauer isotopes, for example, 119Sn, 121Sb, and many of the rare earth elements, but the scope of this volume precludes such extensive coverage We have, however, decided to describe and discuss some special applications of 57Fe M€ossbauer spectroscopy in Chap This is mainly based on work from our own laboratories and we include these to give the reader an impression of the kind of problems that can be examined by M€ ossbauer spectroscopy In Chap 8, we give examples from studies of spin crossover compounds, systems with biological relevance, and the application of a miniaturized M€ ossbauer spectrometer in NASA missions to the planet Mars as well as mobile M€ ossbauer spectroscopy on earth Finally, Chap is devoted to the most recent developments in the use of synchrotron radiation for nuclear resonance scattering (NRS), both in forward scattering (NFS) for measuring hyperfine interactions and inelastic scattering (NIS) for recording the density of local vibrational states A CD-ROM is attached containing a teaching course of M€ossbauer spectroscopy (ca 300 ppt frames), a selection of examples of applications of M€ossbauer spectroscopy in various fields (ca 500 ppt frames), review articles on computation and interpretation of M€ ossbauer parameters using modern quantum-mechanical methods, list of properties of isotopes relevant to M€ossbauer spectroscopy, appendices refering to book chapters, and the first edition of this book which appeared in 1978 In subsequent printruns files are available via springer.extra.com (see imprint page) The authors wish to express their thanks to the Deutsche Forschungsgemeinschaft, the Bundesministerium f u€r Forschung und Technologie, the Max Planck-Gesellschaft Preface vii and the Fonds der Chemischen Industrie for continued financial support of their research work in the field of M€ ossbauer spectroscopy We are very much indebted to Dr M Seredyuk, Dr H Paulsen, and Mrs P Lipp, for technical assistance, and to Professor Frank Berry, for critical reading of the manuscript, and to Dr B.W Fitzsimmons for assistance in the proof-reading Mainz, Muălheim, Luăbeck, November 2010 Philipp Guătlich, Eckhard Bill, Alfred X Trautwein Contents Introduction References Basic Physical Concepts 2.1 Nuclear g-Resonance 2.2 Natural Line Width and Spectral Line Shape 2.3 Recoil Energy Loss in Free Atoms and Thermal Broadening of Transition Lines 2.4 Recoil-Free Emission and Absorption 2.5 The M€ ossbauer Experiment 2.6 The M€ ossbauer Transmission Spectrum 2.6.1 The Line Shape for Thin Absorbers 2.6.2 Saturation for Thick Absorbers References 10 13 17 18 21 23 24 Experimental 3.1 The M€ ossbauer Spectrometer 3.1.1 The M€ ossbauer Drive System 3.1.2 Recording the M€ ossbauer Spectrum 3.1.3 Velocity Calibration 3.1.4 The M€ ossbauer Light Source 3.1.5 Pulse Height Analysis: Discrimination of Photons 3.1.6 M€ ossbauer Detectors 3.1.7 Accessory Cryostats and Magnets 3.1.8 Geometry Effects and Source–Absorber Distance 3.2 Preparation of M€ ossbauer Sources and Absorbers 3.2.1 Sample Preparation 3.2.2 Absorber Optimization: Mass Absorption and Thickness 3.2.3 Absorber Temperature 25 25 27 29 31 34 35 37 41 43 45 46 49 52 7 ix Hartree eV cmÀ1 kcal molÀ1 K J Hartree 27.21138386 219,474.63 627.503 315,775 4.35974  10À19 eV 0.03674932254 8065.54 23.0609 11,604.5 1.60217  10À19 cmÀ1 4.55633  10À6 1.23981  10À4 0.00285911 1.42879 1.98630  10À23 kcal molÀ1 0.00159362 0.0433634 349.757 503.228 6.95  10À21 K 3.16682  10À6 8.61734  10À5 0.6950356 0.00198717 1.38065  10À23 J 2.29371  10+17 6.24151  10+18 5.03412  10+22 1.44  10+20 7.24296  10+22 Hz 1.51983  10À16 4.13567  10À15 3.33564  10À11 9.53702  10À14 4.79924  10À11 6.62607  10À34 Disclaimer: We cannot guarantee for the correctness of the above tables When accuracy is very important, we recommend using website: http://physics.nist.gov/cuu/Constants/index.html Conversion Factors Energy equivalents: Hz 6.57968  10+15 2.41798  10+14 2.99793  10+10 1.04854  10+13 2.08366  10+10 1.50919  10+33 instead the NIST 554 10 Appendices Appendix I: Physical Constants and Conversion Factors 555 Conversion of magnetic hyperfine coupling constants A into internal fields for 57Fe: When the nuclear spin is decoupled from the electronic spin by application of an external field, the hyperfine coupling, according to (4.76), is defined as ^ H^hfs ¼ ~ I Á A Á hS~i; (I.1) where A is the hyperfine coupling tensor in units of energy and hS~i is the expectation value for the electron spin By using the definition of the internal field according to (4.77) ~int ¼ ÀA Á hS~i=gN mN ¼ ÀAT hS~i; B (I.2) where A/gNmN ¼ AT is the hyperfine coupling constant in units of Tesla, the corresponding magnetic splitting of the nuclear states (Fig I.1) can be written in terms of the Zeeman interaction as ^ ~int : IÁB H^hfs ¼ ÀgN mN~ (I.3) Apparently, the equation holds ^ ^ ~ I Á A Á hS~i ¼ ÀgN mN~ I Á ðÀAT Á hS~iÞ: (I.4) A comparison of both sides of (I.4) yields the sought relation for any component of the A tensor A=energy ¼ gN mN ðAT =fieldÞ: Fig I.1 Nuclear Zeeman effect and magnetically split M€ossbauer spectrum (I.5) 556 10 Appendices Since in general the nuclear g factors are different for ground and excited states of a M€ ossbauer nucleus, the spin state must be quoted when giving numerical values for A in energy (which, however, is usually not necessary for NMR spectroscopy or other ground-state techniques) Thus, for a comparison of A values obtained from M€ ossbauer and NMR or ENDOR spectra, usually the ground state is considered The ground- and excited-state magnetic moments m are tabulated as mg ¼ 0.09062(3) n.m (nuclear magnetons, mN) and me ¼ À0.1549 n.m., respectively (see Table “Properties of Isotopes Relevant to M€ ossbauer Spectroscopy” provided by courtesy of Professor J G Stevens, M€ossbauer Effect Data Center, cf CD-ROM) Considering that nuclear magnetic moments are given by the relation m ¼ gImNI, the nuclear g factors for 57Fe with Ig ¼ 1/2 and Ie ¼ 3/2 are gg ¼ 0.09062  and ge ¼ À0.1549  2/3 With these values and mN taken from the table seen earlier, we obtain for the ground state (I ¼ 1/2) of 57Fe, A=MHz ¼ 1:38152 AT =Tesla or AT =Tesla ¼ 0:723841 A=MHz; (I.6) and for the excited state (I ¼ 3/2) of 57Fe, A=MHz ¼ À0:78716 AT =Tesla or AT =Tesla ¼ À1:27039 A=MHz; (I.7) Note that the values of AT are orders of magnitude larger than the A values given for the hyperfine splitting of an EPR spectrum (or ENDOR spectrum) in units of the field sweep necessary to obtain electron spin resonance These are usually on the order of only 101 mT or less! References J Mohr, P., Taylor, N., David, B.N., Newell, B.: Rev Mod Phys 80, 633–730 (2008) Mohr, P.J., Taylor, B.N., Newell, D.B.: J Phys Chem Ref Data 37, 1187–1284 (2008) Index A Absorbers, 45 Absorber optimization, 49 Absorption line, 10, 18 broadening due to absorber thickness, 22 Absorption probability density, 520 Acoustic modes, 518, 523 Acquisition time, 30, 47, 69 ADC See Analog-to-digital converter a-decay, after effects, 413 a-iron (Fe), 32, 56, 81 Amorphous frozen aqueous solution, 204 Analog-to-digital converter (ADC), 36 Ancient rock paintings, 462 Angular dependence, of quadrupole shift, 107 Angular integrals, used for EFG calc., 171 Angular momentum operators, 78 Anisotropy, of covalent bonds, 100 constant, for magnetic particles, 507 LambMoăssbauer factor, 495 molecular vibrations, 520 vibrational behavior, 495 Annihilation of a single phonon, 211 Annulene, 427 Antiferromagnetic transition, 406, 510 Antiferromagnets, 226 a-particle-X-ray spectrometer (APXS), 449, 451, 457 Aperture of a spectrometer, 43 Applied field, 102–112, 124, 406 Applied hydrostatic pressures, 401 APS, 535 APXS See a-particle-X-ray spectrometer Aqueous processes on Mars, 455 Archaeological, 461 Archaeological artifacts, 460 Arrhenius plot, 489 Asymmetry parameter (), 92, 97–99, 164–174, 501 A tensor, 125–127, 423 Atomic units, 139 Atom-selective vibrational spectroscopy, 517 Auger electrons, 39, 40, 63, 450 A-values, 127 Average hyperfine field, 209 Axial and rhombic contribution to ZFS, 124 B Backdonation bonding, 87 Backscattering measurement, 58 measurement geometry, 59, 60, 65, 67, 449 Moăssbauer spectra, 61 Moăssbauer spectroscopy, 60 Basaltic rocks, 65 Basaltic soil, 454 Baseline distortions, 43 b-decay, Bending modes, 520, 523 Benzenedithiolates, 423 Benzene-1,2-dithiolene, 419 Bessel function, 23, 47 Biomimetic model, 498 Bistability, 403 Blocking temperature, 221, 223, 505 B3LYP (DFT computation), 154, 156 Boltzmann factors, 127 Bond lengths, influence on isomer shift, 88 Bond rupture, 413 Born–Oppenheimer approximation, 122 Born–Oppenheimer equations, 138 Boson peak, 526 Bragg scattering, 14 P G€utlich et al., M€ ossbauer Spectroscopy and Transition Metal Chemistry, DOI 10.1007/978-3-540-88428-6, # Springer-Verlag Berlin Heidelberg 2011 557 558 Breit–Wigner equation, 10 Brilliance, 477 Brillouin function, 209 Broadening of resonance lines, 22 C Cage rattling, 526 Calibration approach, 150 constant, of isomer shift, 81 factor, 31 of velocity scale, 31, 66 Calorimetric measurements, 404 Canted spin structures, 229 Carborane, 423 Catalase, 432 CEMS See Conversion electron M€ ossbauer spectroscopy Change of spin-state, 393 Channel advance, 26 Charge density, 77 Charge-sensitive preamplifiers, 68 Chatt-cycle, 443 Checking the authenticity, 461 Chemical and physical after effects, 413 Chromite, 448 Clebsch–Gordan coefficients, 78, 102, 113, 114 Closed-cycle cooler, 42 Coherent electromagnetic waves, 487 Coherent superposition, forward scattered radiation, 494 CO-ligated center, 445 Collective magnetic excitations, 223 Collimator, 55 Collimator diameters, 57 CO metmyoglobin, 532 Combined hyperfine interaction, 103 Completeness of ST, 411 Compositional calibration target (CCT), 62 Compton distribution, 58 Compton scattering, 20, 38, 45, 49, 68 Configuration, 392 Configuration interaction, 146 Constant acceleration mode, 25, 28, 30 Contracted Gaussians, 155 CONUSS, 482 Conversion coefficient a, 20 Conversion-electron detector, 416 Conversion electron Moăssbauer spectroscopy (CEMS), 40 Conversion electrons, 8, 39, 61, 450 Cooperative interactions, 396 Index Coordination compounds, 430 Core polarization, 167 57 Co/Rh, 55 Correlation diagram, for isomer shifts, 84 Corroles, 437 Cosine smearing, 44, 45, 56, 60, 61, 450 Coulomb constant, 80 Counter resolution, 41 Counting statistics, 47 Coupled-cluster theory, 146 Coupled-electron pair approaches, 146 Covalency, 100 Covalent bonding, 86 Covalent ligands, 84 Creation of a single phonon, 211 Critical relaxation time, 205 Critical temperature, 510 Cross-relaxation, 214, 216 Crosstalk, 57 Cryogen-free cryo-cooler systems, 42 Cryo-magnets, 42 Cryostats, 41 Crystal anisotropy, 118 Crystal-field ground states, 429 Crystal field splitting, 211 Crystal-field states, 429 Crystal field theory (CFT), 121 133 Cs, 535 Current integration, 39 Cyanide-ligated, 445 Cyclam, 439 Cytochrome P450cam, 501 D Data acquisition, 26 Data processing, 55 Debye frequency, 15 Debye model, 15, 17, 82, 83, 211, 485 Debye relaxation, 491 Debye temperature, 15–17, 83, 486, 490 Debye–Waller factor, 14 Decay scheme, 34 Delayed electromagnetic radiation, 505 Delayed radiation, 480 Delocalized collective motions, 528 Density functional theory (DFT), 146, 180 Density matrix, 144 Deoxy-metmyoglobin, 532 Deoxymyoglobin, 483, 486 Depth-selective conversion electron Moăssbauer spectra (DCEMS), 40, 64 Depth selective information, 458, 460 Index Depth sensitivity of MIMOS II, 65 Destructive interferences, 505 Detailed balance, 517 Detection of XRF lines, 69 Detector calibration, 67 Deuterated systems, 396 Diamagnetic iron, 498 Diamond-anvil cell, 508 Diamond core, 434 Differential amplifier, 28 Dilution with Zn and Co, 396 Dinuclear complex, 403, 408 Dioxygenase, 433 Dipolar magnetic hyperfine interaction, 183 Dipole interaction, 73, 202 Diradical complexes, 421 Direct-perturbation theory, 148 Dithiocarbamato complexes, 419 Dithiolene, 419 Doppler broadening, 9, 13, 14, 17 Doppler effect, 1, 17, 18 Doppler energy, 12 Doppler modulation, 19, 27 Doppler shift, 13 Doppler velocities, 10, 18, 32 Double-loudspeaker arrangement, 57 Douglas–Kroll–Hess transformation, 148 Drickamer, H.G., 396 Drive coil, 27 Drive control unit, 25–27 Drive performance, 28 Drive system, 57 3d shielding, 87, 163 D-tensor, 186 D-values, 432 Dwell time, 29 161 Dy, 535 Dynamical beats, 480, 482 Dynamically induced temperature-dependence of quadrupole splitting, 487 Dynamical structural disorder, 487 Dynamic distribution, 487 Dynamic processes, 487 E Earth, 447 Easy-axis of magnetization, 108, 224 EC See Electron capture Effective absorber thickness, 21 Effective hyperfine field (Heff), 404 Effective mass, 16, 82 559 Effective nuclear g-factors, 111 Effective thickness, 23, 46, 480, 482, 484 Effect of light irradiation (LIESST Effect), 399 Effect of nuclear decay, 413 EFG See Electric field gradient Einstein model, 212, 214 Einstein temperature, 212 Elasticity theory, 396 Electric field, 74 Electric field gradient (EFG), 74, 89–91, 95, 97, 99, 164, 408, 423, 487 Computation of EFG, 95 Electric field gradient tensor, 76, 107, 166 Electric field gradient tensor element, 174 Electric-field vector s of the incoming beam, 505 Electric monopole interaction, 73, 75, 79 Electric potential, 90 Electric quadrupole interaction, 76, 89 Electron capture (EC), 413 Electron configurations, 101 Electron densities, 79, 144, 151, 156 Electron density at the iron nucleus, 154 Electronegativity, 86 Electron–electron repulsion, 139 Electronics printed-circuit board (PCB), 54 Electronic structure theory, 138 Electrostatic energy, 74 Electrostatic interaction, 73 Emission line, 10, 18 Emission spectrum (g-emission), 34 Energy domain, 477 Energy of g-ray transition, 236 Entropy change upon spin transition, 526 Enzymes, 428 eq, EFG coupling constant, 92 Error signal, 28 ESA See European Space Agency ESA Mars-Express Beagle 2, 53 ESRF, 535 151 Eu, 535 European Space Agency (ESA), 54 Exchange coupling constant, 128, 131, 203 Exchange interactions, 202 Exchange splitting, 143 Expectation values of EFG, 99 Expectation values of spin S, 404 Experimental line width, 22 Extent of cooperativity, 393 Extremely small natural line width, 256 560 F Facial triade, 433 Factorization of the LambMoăssbauer factor, 525 Fast spin relaxation, 128 Fe(0), 85, 440–447 57 Fe, 535 [Fe(bpym)(NCS)2]2(bpym), 403 [Fe(bt)(NCS)2]2(bpym) (bt = 2,2´-bithiazoline), 403 [Fe(HB(3,5-(CH3)2pz)3)2] (pz = pyrazolyl), 395 Fe(I), 85, 169, 440–447 Fe(II), 85, 154, 169, 179, 192–195, 392–416, 425–428, 440–447, 499 Fe(III), 85, 154, 166, 169, 179, 189–192, 417–425 Fe(IV), 85, 154, 166, 172, 184, 428–438 Fe(V), 85, 152, 154, 429, 438–439 Fe(VI), 85, 154, 429, 439–440 [Fe(mtz)6] (BF4)2 (mtz = 1-H-methyltetrazole), 400 [Fe(phen)2(NCS)2], 413 Fe-bearing phases, 448 [Fe(ptz)6](BF4)2 (ptz = 1-H-propyltetrazole), 399 [Fe(2-pic)3]Cl2ÁC2H5OH, 400, 401 [Fe(2-pic)3] Cl2ÁC2H5OH deuterated, 399 [Fe(2-pic)3]Cl2ÁSol, 396 [Fe(phen)3](C1O4)2, 413 Feedback gain, 57 Feedback loop, 28 [FeFe]-hydrogenases, 444 [Fe]-hydrogenase, 445 [FeII(phen)2(NCS)2] (phen = 1, 10-phenanthroline), 394 [Fe2II(PMAT)2](BF4)4ÁDMF, 407 [Fe2II (PMAT)2](BF4)4ÁDMF (PMAT: 4-amino-3,5-bis-4H-1,2,4-triazole), 406 FeIV¼O group, 432 Fe-meteorites, 448 Fe-mineralogical composition, 65 FeMo-cofactor, 532 Fe–Ni alloy, 448, 458 Fermi contact contribution, 180 Fermi contact field, 103 Fermi contact term, 178 Ferredoxins, 130, 529 Ferrimagnetic, 229 Ferrimagnets, 225 Ferrites, 229 Ferritin, 505 Ferrocene, 490 Index Ferromagnetic ordering, 419 Ferromagnetic ordering temperature, 511 Ferromagnetic transition, 510 Ferromagnets, 225 FeS4-centers, 529, 530 Fe4S4-centers, 529 Fe3+ sulfate, 448 [Fe3(iptrz)6(H2O)6](Trifl)6, 408, 409 Field gradient tensor element, 174 Fine structure constant, 148 First-order quadrupole effect, 106 First-order quadrupole shift, 107 Five-coordinate ferric compounds, 420, 424 Fluctuating hyperfine fields, 207 Fock matrix, 142 Fock-operator, 140 Folding, of spectra, 30 Force field, 187 Formalism, 499 Formal oxidation state, 428 Fougerite mineral, 460 Four-coordinate, 425 Four-coordinate low-valent iron(I), 443 Fractional absorption, 23, 47 Frozen solution, 483 Function generator, 25–27 G Gaussian, 22 Gaussian distribution, 13, 41 g-detectors, 26, 38 73 Ge, 535 GeigerMuăller counter, 38 Geometry effects, 43 Glasses, 526 Glass–liquid transition, 490, 528 Goethite (a-FeOOH, GT), 448, 454, 463 Gold (197Au), 348 Goldanskii–Karyagin effect, 118, 495 Gold in medicine, 361 Gravitational red shift experiments, 262 Green rust, 460 GT See Goethite g-tensors, 185 Guanidinium nitroprusside, 495, 520 Gusev Crater, Mars, 451 H Hafnium (176,177,178,180Hf), 285 Half-integer spin, 94 Half-life of excited nuclear state, 236 Hartree–Fock orbital energies, 149 Index Hartree–Fock theory, 139 HASYLAB, 535 H-cluster, 444 HDVV operator, 128 He/4He refrigerators, 42 Heisenberg, W., 128 Heisenberg natural line width, Heisenberg uncertainty relation, Hematite, 56, 64, 448, 454, 458, 460, 463 Heme complexes, 532 Heme proteins, 532 High detection efficiency, 448 High-field condition, 104 High-heat-load premonochromator, 478 High oxidation states, 428 High-pressure investigations, 508 High-resolution monochromator, 478 High-spin iron–oxo, 433 High-valent iron, 429 High-valent iron dimers, 434 High-voltage supply, 26 Hindered rotations, 526 Hohenberg–Kohn theorems, 146 Horseradish peroxidase, 430 Horse spleen ferritin, 222 Hydrogenases, 444, 446 Hydrotris(1-pyrazolyl)borate, 395 Hyperfine coupling, 125 Hyperfine coupling constants, 130 Hyperfine coupling tensor (A), 126, 432 Hyperfine field, 444 fluctuating hyperfine field, 207 Hyperfine interactions, 7, 73 combined hyperfine interaction, 103 Hyperfine interaction tensor, 203 Hysteresis, 493 Hysteresis loop, 403 I 129 I, 535 IDD See Instrument deployment device Ilmenite, 448 Iminothiobenzosemiquinonates, 423 Incoherent superposition, forward scattered radiation, 494 Induced magnetic hyperfine fields, 225 Inelastic excitations, 517 Inhomogeneous line broadening, 22, 47 In situ exploration of extraterrestrial bodies, 67 In situ monitoring of airborne particles, 459 561 of soils below the surface, 460 Instrument deployment device (IDD), 54, 55 Instrument internal calibration, 54, 449 Integer-spin, 94 Integral low-energy-electron Moăssbauer spectroscopy (ILEEMS), 41 Intensity asymmetry, 400, 407 Interacting nanoparticles, 228 Interference pattern, 505 Intermediate fields, 392 Intermediate ligand fields, 413 Intermediate spin, 417, 418, 425, 427 Intermediate spin relaxation, 128 Intermolecular interactions, 526 Intermolecular vibrations, 523 Internal conversion, Internal conversion coefficient, Internal conversion electrons, 63 Internal dedicated microprocessor, 54 Internal magnetic fields, 112 126, 130, 132 Internal reference absorber, 449 Internal reference standards for MIMOS II, 56 Internal source for molecular excitation, 414 Interparticle interactions, 226 Intersystem crossing processes, 399, 415 Intracellular iron storage, 505 Intramolecular antiferromagnetic coupling, 403 Iptrz (4-isopropyl-1,2,4-triazole), 408 193 Ir, 535 Iridium (191,193Ir), 320 Iron(I) See Fe(I) Iron(II) See Fe(II) Iron(III) See Fe(III) Iron(IV) See Fe(IV) Iron(V) See Fe(V) Iron(VI) See Fe(VI) Iron-carbonyl compounds, 440, 441 Iron-containing silicates, 460 Iron(III) halide complexes, 419 Iron(IV)-halides, 430 Iron meteorite, 459 Iron(IV)-nitrido, 428, 435 Iron(IV) oxides, 430 Iron(IV)-oxo, 429, 432, 433 Iron(V)-oxo, 438 Iron(IV)-radical, 430 Iron–sulfur-cluster-free hydrogenase, 445 Iron–sulfur clusters, 86 Iron–sulfur proteins, 130, 529 Irreducible representations, 522 562 Isomers, 79 Isomer shift (chemical shift), 32, 73, 76, 79, 80, 83, 85, 150, 151, 159, 394, 423, 430, 432, 497 influence of bond length, 88 interpretation, 162 calibration constant, 80 correlations, 83–86 correlation diagram, 84 enormously large changes in Ta compounds, 292, 295 references, 32 reference scale, 81 Isonitrosyl structure, 523 Isotopes, table, 557 Isotope effect, 396 Isotope enrichment, 52 Isotope-selective technique, 534 Isotropic relaxation, 209 J Jarosite, 448, 454, 455 K 40 K, 535 Kamacite, 448, 458 K-capture, KEK-AR, 535 K4[Fe(CN)6], 413 83 Kr, 535 Kramers’ degeneracy theorem, 94 Kramers doublets, 94, 111, 203 L LambMoăssbauer factor, 2, 9, 14, 16, 83, 118, 409, 480, 485, 525 Lande´ splitting factor, 404 Langevin function, 223 Larmor frequency, 127 Larmor precession time, 205 Laser calibration, 32, 33 Laser interferometer, 33 Lattice contribution, 97, 171 Lattice vibrations, 15, 127 Librations, 526 LIESST See Light-Induced-Excited-SpinState-Trapping Lifetime of nuclear excited states, 10 of light-induced excited spin states, 400 Ligand field, 392, 417 Ligand field theory (LFT), 121 Light-induced conversion, 402 Index Light-Induced-Excited-Spin-State-Trapping (LIESST), 399, 401, 402, 413, 415 Linear response theory, 149 Linear response treatment, for isomer shifts, 160 Line broadening, 14, 43, 44, 209 Line intensities, 102 Line shape, 9, 21 Line widths, 9, 31 Liquid crystallinity, 411 Liquid-crystal properties, 411 Local contribution, to EFG, 98 Local distortions, 408 Local effective field, 406 Longitudinal relaxation, 206 Lorentzian, 18, 22, 206 Lorentzian lines, 31, 209 Loudspeaker type velocity transducer, 56 Lower limit for the effective thickness, 49 Low-field condition, 108 Low–low-spin, 429 Low oxidation states, 440 Low power consumption, 448 Low-spin (LS), 84, 444, 392 Low-valent iron, 440 Low-valent iron porphyrins, 44 M Macrocycles, 423 Maghemite, 56 Magic angle of 54 , 407 Magnetically-induced quadrupole splittings, 177 Magnetically perturbed quadrupole spectra, 109 Magnetic anisotropy, 220, 506 Magnetic coupling, interplay with spin transition, 403 Magnetic dipole, 102 transition, 114 Magnetic hyperfine coupling, 125, 178 Magnetic hyperfine coupling tensor, 126, 500 Magnetic hyperfine interaction, 102, 178, 503 Magnetic hyperfine interaction in paramagnetic iron, 498 Magnetic hyperfine splitting, 102 Magnetic hyperfine tensors, 126, 423 Magnetic interaction, 498 Magnetic interaction in diamagnetic iron complex, 498 Magnetic moments of HS, 393 Magnetic nanoparticles, 220 Magnetic ordering temperatures, 510 Magnetic perturbation, 94 Index Magnetic properties, 407 Magnetic relaxation, 201 Magnetic resonance methods, 393 Magnetic shielding, 57 Magnetic splitting, 102, 103, 406 Magnetic susceptibility, 125, 393, 407 Magnetite, 56, 448, 460 Magnetocrystalline anisotropy, 220 Magnets, 41 Magnets for longitudinal fields, 43 Main amplifier, 26 Main components of the EFG, 91 Many body perturbation theory, 146 Mars, 62 Mars Exploration Rovers (MER), 447 Martian dust, 65 Martian surface temperatures, 58 Mass absorption coefficients, 20, 49, 50 MC See Monte-Carlo (MC)-simulation Mean lifetime, 8, Mean-square displacement (MSD), 82, 478 Mean-square nuclear radius, 236 Mean square radius, 79 Mean square velocity, 82 Mercury (199,201Hg), 373 Meridiani Planum, 454 Meridiani Planum Moăssbauer mineralogy, 456 MES See Moăssbauer emission spectroscopy Metal-containing liquid crystals, 411 Metal–donor atom distance, 393 Metallomesogens, 411 Metalloproteins, 430 Metal–organic compounds, 440, 441 Metastable HS state, 401, 403, 413 Metastable LS state, 399 Metastable states, 413 Meteorites, 455 Meteorites on Mars, 455 Metmyoglobin single crystal, 533 Michelson interferometer, 33 Microcontroller IP, 68 Microscopic imager (MI), 449, 451 MIMOS II, 53, 54, 60, 64, 447, 448, 459, 460 MIMOS IIA, 68 advanced instrument MIMOS IIa, 67, 463 terrestrial applications, 459 MIMOS II sensor head (SH), 55 MIMOS II temperature sensors, 63 MIMOS in space, 447 Mineralogy, 452 Miniaturized Moăssbauer spectrometer, 53 Miniaturized spectrometer MIMOS II, 53 Minimal thickness, 48 563 Mixed spin-state pairs, 404 Mixed hyperfine interaction, 103 Mobile Moăssbauer spectroscopy, 447 Mode composition factor, 518 Mode coupling theory, 490 Molecular crystals, 526 Molecular dynamics, 490 Molecular orbital diagram, 88 Molecular properties, 149 Molecular structure, 407, 409 Mono complexes, 421 Monte-Carlo simulation, 64, 65, 454 Morin transition, 454 Moăssbauer backscattering spectra, 461 Moăssbauer detectors, 37 Moăssbauer drive, 25, 27, 55 Moăssbauer effect, 1, 8, 18 Moăssbauer emission spectroscopy (MES), 267, 413 Moăssbauer experiment, 17 Moăssbauer light source, 34 Moăssbauer measurement in applied field, 125, 404 Moăssbauer parameters, 73110, 431 Moăssbauer periodic table, Moăssbauer source experiments, 413 Moăssbauer sources, 25, 27, 45, 55 Moăssbauer spectrometers, 25 Moăssbauer spectroscopy in time domain, 477 Moăssbauer spectrum, 29 Moăssbauer temperature, 17, 82, 83 Moăssbauer time window, 415 Moăssbauer transmission experiment, 19, 43 Moăssbauer transmission spectrum, 18 MOTIF, 482 Multi-channel analyzer, 26, 29 Multipolarity of g-radiation, 236 Multipole expansion, 73 Multipole transitions, 113 N Nanophase ferric oxides, 453, 454 NASA Mars-Exploration-Rover, 53, 54, 448 Natural abundance, 236, 557 Natural line width, 9, 10, 14, 31, 236 145 Nd, 535 Ne´el–Brown expression, 220 61 Ni, 535 Nickel (61Ni), 237 [NiFe]-Hydrogenases, 445 61 Ni Moăssbauer emission spectroscopy, 250 NIS See Nuclear inelastic scattering Nitrogenase, 532 564 NMR, Noncubic lattice, 100 Nonheme enzymes, 433 Noninnocent ligands, 437 Noninteracting particles, 220, 228 Nonlinear baseline distortion, 44 Nonnitrido-iron(IV), 436 Nonoxo-iron(IV), 436 Nonplanar porphyrinates, 422 Nonrelativistic, 165 Normalized elimination of the small component (NESC), 148 Normal mode composition factors, 191 Normal mode compositions, 192 Normal modes, 187, 192, 522 NQR See Nuclear quadrupole resonance NRVS See Nuclear resonance vibrational spectroscopy and nuclear inelastic scattering Nuclear charge density, 74 Nuclear data, 557 Nuclear Decay Induced Excited Spin State Trapping (NIESST), 414 Nuclear decay process, 236 Nuclear electric quadrupole moment, 236 Nuclear forward scattering (NFS), 209, 479, 483 Nuclear g-resonance, 7, Nuclear hyperfine interactions, 73, 102, 125 Nuclear inelastic scattering (NIS), 186, 477, 516 intensity, 187 spectrum, 189 Nuclear lighthouse effect, 511 Nuclear magnetic dipole moment, 236 Nuclear magneton, 102 Nuclear monopole moment, 75 Nuclear–nuclear repulsion, 139 Nuclear potential, 87 Nuclear quadrupole moment, 75, 76, 90 Nuclear quadrupole resonance (NQR), 89 Nuclear radius, 80 Nuclear resonance absorption, Nuclear resonance absorption of g-rays, Nuclear resonance inelastic X-ray scattering, 517 Nuclear resonance scattering, 477 Nuclear resonance vibrational spectroscopy (NRVS), 186, 517 Nuclear resonant forward scattering (NFS), 477 Nuclear spin quantum number, 236 Nuclear states, 78 Index Nuclear Zeeman effect, 102 Nucleogenic 57Fe, 413 Nucleogenic 57Fe(II), 414–415 O Octahedral crystal field, 418 Octahedral iron complex, 423 Olivine, 64, 448, 451, 453, 454 Olivine-bearing basaltic soil, 455 One-electron Hamiltonian, 140 One-electron integrals, 140 Opportunity, 53, 447, 451 Optical spectroscopy, 393 Orbach process, 212 Orbital contributions, 113 Orbital moment, 103 Orbitals, 140 Orientation-dependent line-intensity ratio, 495 Osmium (186,188,189,190Os), 310 Output response voltage, 26 Oxoferrates, 430 Oxo groups, 428 Oxygenases, 428 Oxymyoglobin, 487 P p-acceptor, 84 Paramagnetic iron, 120131, 498 Paramagnetic Moăssbauer spectra, 121 Paramagnetic picket-fence porphyrin complex, 500 Paramagnetic relaxation processes, 210 Paramagnetic relaxation time, 209 Paramagnetic systems, 120–131 Partial density of vibrational states (PDOS), 186, 188, 194, 516 Partition function, 406 Pauli principle, 140 p-backbonding, 86 PDOS See Partial density of vibrational states Permanent magnets, 57 Perovskites, 430 Peroxidases, 428 Perturbation theory, 148 Perturbation treatment, 104 Phonon annihilation, 517 Phonon-assisted Moăssbauer effect, 517 Phonon-assisted nuclear resonance absorption, 517 Phonon creation, 517 Phonon polarization vector, 518 Phonons, 127 Phonon spectrum, 211 Index Photo and thermochromism, 411 Photo effect, 20, 49 Photoswitching processes, 399 Phthalocyanine, 425, 426 Picket-fence porphyrin, 483, 498, 532 Pick-up coil, 27 Piezoelectric quartz drive system, 256 Piezoelectric transducers, 27 Pigment characterization, 461 Pigments, 461, 463 PIN diodes, 39 Planar four-coordinate, 418 Plateau, of spin transition curve, 407 Platinum (195Pt), 339 Point-charge contributions, 170 Point charges, 95 Poisson distribution, 48 Poisson’s differential equation, 76 Polar angles, 114 Polarity of the Moăssbauer drive, 33 Polarization, 502, 505 Polycrystalline material, 483 Porphyrinates, 419, 424 Porphyrines, 423 Porphyrin radical, 442 Position adjustable workbench (PAW), 55 Potassium ferrocyanide, 31 Potential energy surface, 138 Potential Moăssbauer isotopes for nuclear resonance scattering, 534 Potential wells, 393 Power consumption, 69 p-radical form, 422 Preamplifier, 26 Precursor nuclide, 236 Pressure dependence of 57Fe Moăssbauer spectra, 400 Pressure-dependent NFS measurements, 510 Principal axes system (PAS), 91 Produkt Ansatz, 140 Projected mean square displacement, 523 Proportional counters, 37 Protein dynamics, 528 Pulse amplifier, 26 Pulse discrimination device, 26 Pulse height analysis (PHA), 35 Pulse-height analysis (PHA) spectrum, 59 Pulse height spectrum, 36 Pyrite, 64, 460 Pyroxene, 448, 451, 453 Q Quadrupole doublet, 93 Quadrupole interaction, 73, 77, 78, 93, 171 565 Quadrupole moments, 78, 89, 91 Quadrupole shifts, in magnetic spectra, 106 Quadrupole splittings, 77, 92, 93, 164, 394, 423, 432, 480 Quantum-beat pattern, 487, 497 Quantum beats, 480 Quantum chemistry, 137 Quantum mechanical formalism, 77 R Radial distribution function, 182 Radial wavefunctions, 168, 169 Radiationless emission, Radiationless relaxation, 401 Radical, 423 Raman processes, 211, 212, 214 Random jump cone, 515 Rapid-freeze quench technique, 433 Rattling of molecules, 491 Raw spectra, 30 Rayleigh–Ritz functional, 140 Rayleigh scattering, 183W 46.5 keV Moăssbauer radiation, 309 Recoil, Recoil effect, 12 Recoil energy, 11, 236 Recoil energy loss, 10 Recoil-free fraction (fs), 14–18, 20, 35, 47, 82 Recoilless emission and absorption, Recoilless nuclear resonance absorption (fluorescence), 1, Recoil momentum, 11 Redox processes, 413 Reduced energy-gap law, 415, 417 Reference absorber, 59 Reference materials, 33, 81 Reference scatterer, 497 Reference voltage, 26, 27 Relative absorption depth, 47 Relative line intensities, 34, 113, 118 Relative resolution, 41 Relativistic effects, 81, 148, 149 Relativistic quantum mechanics, 81 Relativistic shift, 82 Relaxation, 127 Relaxation effects, 487 Relaxation model, 210 Relaxation pathways, after LIESST, 415 Relaxation rates, 489, 503, 504, 515 Relaxation scheme, 416 Relaxation spectra, 205 Relaxation times, 205 Resolution of detector, 41 Resonance detector, 416 566 Resonance cross-section (s0), 46, 47 Resonant absorption, Resonant absorption cross section, 236 Restricted open-shell HF (ROHF), 144 Reverse LIESST, 399, 401 Rhombicity parameter, 124, 500 Rhombic monopyramidal, 418 Rhombic-pyramidal, 419 Rhombic-pyramidal five-coordinate, 418 Rieske dioxygenases, 438 Robotic arm, 449 Rock abrasion tool (RAT), 451 Rock Adirondack, 453 Rock paintings in the field, 461 ROHF See Restricted open-shell HF Rotational dynamics, 514 Rovers, Spirit and Opportunity on Mars, 62, 451 Rubredoxins, 529, 530 Ruthenium (99Ru, 101Ru), 270 Ruthenium brown, 276 Ruthenium red, 276 S Sample, preparation, 46 elemental composition, 67 Sampling depth, 62, 63, 450 Saturation, 22, 23 Saw-tooth mode, 25 Saw-tooth motion, 25 121 Sb, 535 Scalar-relativistic, 165 Scattered radiation, 45 Schreibersite, 448, 459 Schroădinger equation, 138 Scintillation counters, 38 SCO See Spin crossover Second-order Doppler shift, 17, 31, 81, 238 Selective spin switching, 410 Semiempirical methods, 161 Semiquinonate, 421 Sensor-head (SH), 54, 63, 449, 460 Sensor molecule, 514 Separation of I-and S-contributions, 126 Shape anisotropy, 220 Shielding, 55, 87 Shielding effect, 162 Signal-to-noise ratio (SNR), 30, 50, 68 Sign of EFG tensor, 95, 107, 109 Silicon-drift-detectors (SDD), 39, 67, 68 Simultaneous acquisition of the XRF spectrum, 67 Single-channel analyzer, 26 Single-crystal measurements, 94 Index Single-line absorber, 413 Sinusoidal operation, 25 Si-PIN detectors, 55 Si-PIN-diodes, 58 Six-coordinate, 428 Six-coordinate ferric compounds, 420 Slater determinant, 140 Slater-type orbitals, 155 Slow paramagnetic relaxation, 202 Slow spin relaxation, 128 149 Sm, 535 119 Sn, 535 SOC See Spin–orbit coupling Sodium ferrocyanide, 81 Sodium nitroprusside, 31, 81 Solid–liquid crystal phase transition, 411 Solid-state detectors, 39 4s orbital, 159 4s orbital population, 163 Solvent effects in spin transition, 396 Source-absorber distance, 43 Source activity, 55 Source experiment, 45 Spectral fitting routines, 451 Spectral line shape, Spectrometer aperture, 44 Spectrometer resolution, 41 Spectrometer tuning, 28 Spin, 84, 89, 92, 102, 111, 120–131, 142, 185, 202, 211, 214, 503 Spin admixture, 424 Spin allowed d–d transitions, 401, 415 Spin-allowed excitation, 399 Spin-canting, 229 Spin coupling, 128 Spin-coupling scheme, 129 Spin crossover (SCO), 392, 393, 403, 408, 411 Spin–crossover complexes, 392, 491, 523 Spin-density, 144 Spin-dipolar contribution, 103 Spin–dipolar interaction, 178 Spin flips, 505 Spin-Hamiltonian, 124, 202, 498 Spin-Hamiltonian concept, 121 Spin-Hamiltonian formalism, 121 Spin-Hamiltonian operator, 78 Spin-Hamiltonian parameters, 425 Spin–lattice relaxation, 127, 210, 211, 503 Spin–lattice relaxation frequency, 214 Spin multiplicity, 392 Spin–orbit correction, 178 Spin–orbit coupling (SOC), 100, 122, 148, 175, 178, 183, 415, 424 Spin-polarization, 103, 142, 143, 180–182 Index Spin projection coefficients, 131 Spin quantum number, 78 Spin-quartet ground state (S ¼ 3/2), 417 Spin relaxation, 42, 53, 128 Spin-sextet, 417 Spin–spin relaxation, 127, 203, 210, 214 Spin state conversion, 408 Spin transition (ST), 393 influence of pressure, 396 sensitive to external pressure, 396 spin conversion, 404 two steps, 396 Spin-triplet ground state, 423 Spirit, 53, 447, 451 Split-pair magnets for transversal fields, 43 SPRING-8, 535 Square-planar, 425 Square-pyramidal, 417, 419 Square-pyramidal five-coordinate, 418 32 36 S/ S isotope replacement, 531 ST See Spin transition Standard beamline equipment, 478 Stress anisotropy, 220 Stretching modes, 519, 520, 523 Strong fields, 104, 392 Strong ligand fields, 413 Structural transition and liquid crystallinity interplay, 411 Sulfur-ligands, 419 Sulfur-rich outcrop, 454 Superconducting cryo-magnet, 42 Superexchange, 128 Superparamagnetic relaxation, 220, 505 Surface anisotropy, 220 Synchrotron radiation, pulses, 479 sources, 534, 535 Synchrotron radiation based perturbed angular correlation (SRPAC), 512 SYNFOS, program package for NRS, 482, 499 T Table of Isotopes, 557 Tantalum (181Ta), 289, 535 125 Te, 535 Temperature-dependent NIESST experiments, 416 Temperature-dependent quadrupole splitting, 175, 484, 486 Temperature sensors, 449 Tetraazaporphyrines, 423 Texture effects, 120, 400, 401, 407 Thermal broadening, 9, 10 Thermal emission spectrometer, 457 567 Thermal hysteresis, 393 Thermal relaxation, 403 Thermal spin transition, 411 Thermodynamic approach, 396 Thick absorbers, 23 Thickness, 49 broadening, 22, 47 of surface layer, 64 Thin absorber approximation, 47 Thin absorbers, 21 Thin films, 411 Thiocarbamates, 423 Thiooxolates, 423 Thiosalen, 423 Thiosemicarbazides, 422, 423 Three-coordinate low-valent iron(I), 443 Time-delayed coherent electromagnetic radiation, 479 Time-differential NFS intensity, 482 Time-differential perturbed angular correlation, 512 Time-integral 57Fe Moăssbauer emission spectra, 414 Time-resolved MES, 415 Time-resolved optical spectroscopy, 415 Time-scale of technique (10À7 s), 394 Time structure, 502 169 Tm, 535 Total internal conversion coefficient, 236 Total spin, 142 129.4 keV transition line of 191Ir, 320 Transition metals suitable for Moăssbauer spectroscopy, 235 Transition probabilities, 113 Transition temperature T1/2, 393 Translational modes, 526 Transmission geometry, 25, 60 Transmission integral, 21 Transversal coherence, 494 Transverse relaxation, 229 Trapping, HS state, 413 Triangular mode, 25 Triangular reference signal, 58 Triangular velocity profile, 28, 30, 57 Trifl (trifluoromethanesulfonate), 408 Trinuclear iron(II) complex, 408 Trivalent iron, 417 (See also Fe(III)) Tuning, of spectrometer performance, 28 Tungsten (180,182,183,184,186W), 301 Time-reversal violation experiment, 284 Two-electron integrals, 140 Two-phonon processes, 211 U Unrestricted Hartree-Fock (UHF), 143 568 V Valence contributions, 98, 162, 163, 168 Valence electrons, 98 Velocity calibration, 31, 32, 66 Velocity linearity, 58 Velocity pick-up coils, 57 Velocity range, 31 Velocity transducers, 27 Vibrational frequencies, 187 Vibrational spectroscopy, 393 Vibronic levels, 393 Victoria Crater, on Mars, 459 Voigt profiles, 23 Vzz, 92 W Water activities, on Mars, 454 Wave vector k, 113 Weak fields, 108, 392 Weak ligand fields, 413 Index Weathering processes, 454 Wigner–Eckart theorem, 78 X X-ray fluorescence (XRF), 34, 35, 45 X-ray line, 35 X-rays, 63, 450 XRF See X-ray fluorescence Z Zeeman splitting, 211 Zero-field spectrum, 406 Zero-field splitting (ZFS), 122, 185, 403, 407, 423, 432, 433, 443, 500 Zero-phonon peak, 516 Zero-phonon processes, 2, 14, 18 Zero-point energy separation, 396 Zero-point fluctuations, 188 Zero’th order regular approximation, 148 ZFS See Zero-field splitting Zinc (67Zn), 255, 535 ...Moăssbauer Spectroscopy and Transition Metal Chemistry Philipp Guătlich Eckhard Bill Alfred X Trautwein l l Moăssbauer Spectroscopy and Transition Metal Chemistry Fundamentals and Applications. .. Moăssbauer Isomer Shifts North Holland, Amsterdam (1978) Gutlich, P., Link, R., Trautwein, A.X.: Moăssbauer Spectroscopy and Transition Metal Chemistry Inorganic Chemistry Concepts Series, vol 3,... t and will undergo a transition to its ground state (g) of energy Eg, according to the exponential law of decay This leads, P G€utlich et al., M€ ossbauer Spectroscopy and Transition Metal Chemistry,